Method and Apparatus for Assay of Electrochemical Properites

ABSTRACT

A method for monitoring a select analyte in a sample in an electrochemical system. The method includes applying to the electrochemical system a time-varying potential superimposed on a DC potential to generate a signal; and discerning from the signal a contribution from the select analyte by resolving an estimation equation based on a Faradaic signal component and a nonfaradaic signal component.

BACKGROUND

The use of electrochemical means of detection has often been chosen forits simplicity, both in terms of device manufacture and in terms of easeof use. The principle mode of selectivity of electrochemistry (both foramperometric and potentiometric modes) is the reduction-oxidation (alsocalled “redox”) potential of the analyte (which is the chemical speciesof electrochemical interest). For example, using the technique ofamperometry (where the potential is applied to the electrode, and theresulting current is measured), the selectivity towards the analyte isachieved based on the redox potential of the analyte.

The signal that is generated at the electrode can depend on many factorsand properties of the electrochemical system. Examples of properties ofthe sample that affect the transport of the analyte include viscosity,temperature, density, and ionic strength. The variations that affect thetransport of the analyte can subsequently affect the measuredelectrochemical signal. Examples of such transport mechanisms includediffusion, migration, and convection.

In another example, the properties of the electrode itself can affectthe transport of the analytes and/or the kinetics of any reactions thatmay generate the measured electrochemical signals. Examples of suchproperties include the effective electrode area, the geometry of theelectrodes, the geometry of the sample chamber, the extent of electrodefouling, diffusional barrier membranes over the electrode, and catalyticproperties of the electrode material.

Electrochemical sensors are commonly found in a number of sensingapplications, from medical biosensors to environmental and gas sensors.There are commonly two modes of electrochemical measurement,amperometric and potentiometric. Amperometric sensors operate on theprinciple of applying a voltage potential to an electrode and measuringthe resulting current. Examples of amperometric sensors include mostcommercial glucose biosensors and many gas sensors. Potentiometricsensors operate on the principle of applying a current to an electrodeand measuring the resulting potential. It is often the case that theapplied current is kept at zero amps. The pH electrode is an example ofa potentiometric sensor.

FIG. 1 shows the action of an amperometric sensor in which a voltage isapplied to the electrode 310 which causes a particular analyte (thesubstance being measured) in the sample to be oxidized (i.e., giving upelectrons to the electrode). The oxidation causes a current 315 to begenerated which can then be detected and analyzed. The potential atwhich the analyte oxidizes is called the “oxidation potential” of theanalyte.

Generally speaking, the term “redox potential” is used to indicate thepotential at which an analyte is either oxidized or reduced. In thesensor of FIG. 1, ferrocyanide (“FERRO”) 300 transfers electrons to theelectrode if the potential is high enough to cause the electrochemicalreaction to occur. Once the electrons are transferred, ferrocyanide isoxidized to ferricyanide (“PERU”) 305.

Thus, in FIG. 1, a sufficiently high potential is being applied tooxidize ferrocyanide, the reduced form of the electroactive species, tothe oxidized form, ferricyanide, and the resultant current 315 detectedby the electrode depends on the concentration of the reduced species.

As discussed above, the current from amperometric sensors depends on anumber of factors in addition to the concentration of the analyte ofinterest. Traditional amperometric methods rely on the assumption thatonly the concentration of the analyte changes from measurement tomeasurement; hence, when other factors of the electrochemical systemvary, the measured signal and the estimate of the analyte concentrationcan be incorrect. Potentiometric sensors also suffer from relatedfactors, including transport of the analyte and electrode fouling.Variations in these factors would add uncertainty and error to themeasured signal. For example, FIG. 2 shows the DC current from twoamperometric sensors where the effective electrode area is changed. Datapoints 455 are measured in a sample containing 10 mM ferrocyanide. Datapoints 450 are measured in a sample containing 20 mM ferrocyanide. Inboth cases, as the electrode area varies, the measured DC current signalvaries as well. Furthermore, for a given electrode area, increasing theanalyte concentration from 10 mM to 20 mM results in measuring anincreased current signal. This illustrates the dependence of themeasured DC current signal on the electrode area and on the analyteconcentration.

Several factors may contribute to a sensor having variable electrodearea. One source may be errors during manufacturing that may lead tovariability in the electrode area from sensor to sensor. Another factormay be deterioration of the electrode during use. Another factor may beincomplete contact of the sample with the sensor electrode, examples ofwhich are illustrated in FIGS. 8 and 9.

FIGS. 8a through 8c are schematic diagrams of a typical electrochemicaltest strip that forms the basis for many commercially available glucosebiosensors. In FIG. 8 a, there are two electrodes 355, each of which isconnected to leads 350 that interface with the electronics of the meter.The electrodes 355 and leads 350 may be coupled to a support substrate375. In this example, the test strip uses a commonly used 2-electrodeconfiguration. In FIG. 8 a, the sample 360 completely covers bothelectrodes, ensuring that the entire electrode area of each electrode isin contact with the sample. In FIG. 8 b, sample 370 covers one electrodecompletely but partially covers the other electrode. In FIG. 8 c, sample365 partially covers both electrodes.

FIG. 9 illustrates partial coverage of electrodes by a sample for adifferent geometry of electrodes. In this example, an electrochemicaltest strip is made with two electrodes facing each other in a parallelplate design. Electrode 400 and electrode 405 are supported by a solidsubstrate material 420. Sample 410 fills the sample chamber and coversboth electrode areas fully. Sample 415, however, only partially coversboth electrode areas and results in a system of reduced effectiveelectrode area. Such incomplete coverage of the electrode surface can bea result of partial filling of the sample chamber. In one example,diabetic patients that make blood glucose measurements must often usesuch electrochemical test strips to make measurements of blood glucose.In such cases, if enough blood does not enter into the sample chamber,incomplete coverage of the electrode system can result, yieldinginaccurate glucose estimates. Thus, a method to assess the effectiveelectrode area that is independent of the analyte concentration would beuseful.

Furthermore, the volume of sample that enters into the test strip can beestimated. Referring to FIG. 9, if the three dimensions of the samplechamber that contains sample 415 are known, then the volume of sample415 can be estimated by scaling the total geometric volume of the samplechamber by the fractional amount of the electrode coverage. In oneexample, the total volume of the sample chamber is 100 nL. If sample 415is determined to cover 75% of the electrode 405, then one estimate ofthe volume of sample 415 would be (0.75)*100 nL=75 nL. The estimate ofthe sample volume would be useful when making measurements that dependon knowing the volume of the sample in the electrochemical cell. Oneexample of where this knowledge would be useful is in coulometry.

FIG. 4 illustrates the problem of electrode fouling with electrochemicalsensors. Electrode fouling, also called sensor fouling, is a term thatdescribes material 320 adhering, adsorbing, or otherwise coating all orpart of the electrode 310. In this example, the analyte is ferrocyanide300 which must move through the fouling material 320 and then react atthe electrode 320 in an oxidation reaction that yields an electroniccurrent 315 in the electrode 310. The product of the reaction isferricyanide 305 which then moves back out of the fouling material 320.One example of when electrode fouling may occur is during extended useof the sensor in environments that could cause fouling, such asimplanting a biosensor into the body or deploying gas sensors inenvironments containing sulfides. In such situations, as well as othersituations that would be apparent to one skilled in the art, materialmay deposit onto the electrode, causing a distorted signal to bemeasured. Often, the measured signal intensity decreases as the amountof electrode fouling increases until ultimately the sensor becomesinsensitive to the target analyte. In other cases, the fouling materialmay act as a catalyst for certain chemical reactions and the sensor'sresponse may actually be enhanced. In either case, if the sensor'sresponse is altered due to fouling, then the resulting measurement isinaccurate.

In the calibration curves shown in FIG. 3, data points 470 measure theDC current from samples with different concentrations of ferrocyanidewith an electrode that is not fouled. Data points 480 measure the DCcurrent from samples with different concentrations of ferrocyanide withan electrode that is fouled by a coating of 3.33 μg of celluloseacetate. Data points 490 measure the DC current from samples withdifferent concentrations of ferrocyanide with an electrode that isfouled by a coating of 10 μg of cellulose acetate. This exampleillustrates that the measured DC current signal in this amperometricsensor depends on both the analyte concentration and the extent ofelectrode fouling. Thus, a low DC signal may be the result of either lowanalyte concentration or due to increased electrode fouling. Thus, ameans to determine the extent of electrode fouling which is independentof analyte concentration would be useful. Such a method could then beused to adjust the measured current signal and correct for signaldistortion caused by electrode fouling.

Although the previous two examples were illustrated with amperometricsensors, one of ordinary skill in the art will recognize the applicationto potentiometric sensors. Potentiometric sensors also rely on analytecoming into the proximity of the electrode.

Thus, when electrochemical means of detection are used, theenvironmental factors—including the properties of the sample thatcontain the analyte—may heavily influence the signal that is measured.Such factors may introduce inaccuracies into the measurement, includingbut not limited to, change in calibration and change in sensitivity.Hence a method and apparatus for detecting properties of the environmentthat may affect the measured signal, including dielectric constant ofthe sample or the electrode, effective electrode area, and ionicstrength of the sample, would benefit electrochemical sensor systems andmay allow for corrections to be made to the estimated analyteconcentration, calculated from the measured signal, based on theinformation about the environmental factors.

SUMMARY OF THE INVENTION

An embodiment of the present invention relates to a method formonitoring a select analyte in a sample in an electrochemical system.The method includes applying to the electrochemical system atime-varying potential superimposed on a DC potential to generate asignal; and discerning from the signal a contribution from the selectanalyte by resolving an estimation equation based on a Faradaic signalcomponent and a nonfaradaic signal component.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate several embodiments of theinvention and together with the description, serve to explain theprinciples of the invention.

FIG. 1 is an amperometric sensor for measuring ferrocyanide;

FIG. 2 is a chart showing the increase in DC current due to an increasein electrode area for two samples with different ferrocyanideconcentration;

FIG. 3 is calibration calibration curves showing the increase in DCcurrent due to increasing concentration of ferrocyanide using threeelectrodes with different extents of fouling.

FIG. 4 is an amperometric sensor for measuring ferrocyanide where theelectrode is fouled;

FIG. 5 is flow diagram illustrating a method for processingelectrochemical signals in accordance with an illustrative embodiment;

FIG. 6 is flow diagram illustrating a method for processingelectrochemical signals in accordance with another illustrativeembodiment;

FIG. 7 is a system for processing electrochemical signals in accordancewith another illustrative embodiment.

FIGS. 8 a, 8 b, and 8 c show three examples of how a sample can makecontact with electrodes for one particular geometric organization ofelectrodes.

FIG. 9 shows two examples of how a sample can make contact withelectrodes for another particular geometric organization of electrodes;

FIG. 10 shows calibration curves for ferrocyanide obtained withelectrodes of two different effective areas;

FIGS. 11 shows a waveform applied to an electrode system in accordancewith an example performed using the methods of FIG. 5 and FIG. 6;

FIG. 12 shows how a vector in the complex plane can be decomposed into areal part and an imaginary part;

FIG. 13 is a chart showing the increase of the imaginary component ofthe AC current with increasing electrode area from measurements madefrom two samples containing different concentrations of ferrocyanide;

FIG. 14 is a chart showing the dependence of the DC current on theextent of electrode fouling from three samples containing differentamounts of ferrocyanide;

FIG. 15 shows how the relationship between the slope and intercept of acalibration curve, that relates concentration of ferrocyanide to DCcurrent, depends on the extent of electrode fouling;

FIG. 16 is a chart showing the amplitude of the AC current for differentconcentrations of ferrocyanide as measured with three electrodes withdifferent extents of fouling;

FIG. 17 shows the value of the AC current for measurements made withelectrodes with different extents of fouling;

FIG. 18 is a glucose meter in accordance with an illustrativeembodiment; and

FIG. 19 is an illustration of a fuel tank containing spatially separatedlayers of petrol and water.

DETAILED DESCRIPTION

Reference will now be made in detail to several illustrative embodimentsof the present invention, examples of which are shown in theaccompanying drawings. Wherever possible, the same reference numberswill be used throughout the drawings to refer to the same or like parts.

Systems and methods are provided herein for improving the accuracy andproductivity of sensors via digital signal processing techniques. Inparticular, in accordance with certain illustrative embodiments, methodsare provided herein for monitoring environmental effects that can affectthe measured sensor signal, e.g. effective electrode area and/or extentof fouling, to correct for measurement errors. In this way, a change inthe measured signal that is due to an environmental factor can besubstantially reduced to more accurately measure the concentration of atarget analyte, such as ferrocyanide.

As used herein, the term “transducer” refers to a substance or apparatusthat converts energy of one form into energy of another form. Examplesof transducers include, but are not limited to, electrodes, lightemitting diodes, photo diodes, piezoelectric material, and microphones.

As used herein, the term “capacitive properties” refers to any and allproperties of a system that may contribute and/or affect the capacitanceof the system and includes, but is not limited to, the electrode area,the dielectric constant, the permittivity, double-layer characteristics,ionic strength of a sample, and the capacitance.

As used herein, the term “blank” refers to a sample that is comprised ofsupporting electrolyte.

As used herein, the term “background” can be used interchangeably withthe term “blank” and refers to the signal that is generated by a blanksample.

As used herein, the term “CDAS” refers to capacitive dominatedadmittance spectra and indicates the frequency range in which theadmittance values of the electrochemical system is dominated by thecapacitive components of the electrochemical system; this may generallybe towards the higher frequency range but may be in other rangesdepending on the characteristics of the particular electrochemicalsystem under consideration.

As used herein, the term “ESS” refers to an electrochemical signalsource, which is an entity in a sample that can give rise to anelectrochemical signal; the term “ESSs” is used to refer to the pluralof ESS. A common ESS is an electroactive chemical species, but theinvention is not limited to the assay of signals only from such sourcesand includes non-electroactive chemical species, background electrolyte,double-layer capacitance, non-chemical sources, and sources not in thesample such as electromagnetic interference, commonly known as RFinterference.

As used herein, the term “ESSI” refers to an ESS that is of interest tobe measured including, but not limited to, chemical species, or thebackground composition of a sample that may give rise to the backgroundor blank signal, or the capacitance that may be measured by thetransducer-sample interface.

The term “variation” as used herein, refers to the absolute value of thedifference between the maximum value and the minimum value of a waveformduring the course of its application.

As used herein, the term “TSI” refers to the transducer-sample interfacethat is comprised of the interface between the transducer and the samplethat may contain a set of ESSs.

As used herein, the term “FFT” refers to Fast Fourier Transform.

As used herein, the term “FT” refers to Fourier Transform.

As used herein, the term “DFT” refers to discrete Fourier Transform.

As used herein, the term “WT” refers to Wavelet Transform.

As used herein, the term “DTH'” refers to discrete time FourierTransform.

As used herein, the term “ADC” refers to an analog-to-digital converter.

As used herein, the term “derived quantities” refers to quantities thatmay be computed with reference to the measured data from theelectrochemical system and external sources of data and/or information.

As used herein, the term “Faradaic” refers to electrochemical reactionsin which electronic charge is transferred across the TSI. Thesereactions refer to an oxidation or reduction of an analyte.

As used herein, the term “effective electrode area” refers to theelectrode area that is in electrolytic contact with the sample. Theeffective electrode area may be varied by altering the geometry of theelectrode or by partial contact of the electrode to the sample.

As used herein, the term “extent of electrode fouling” refers to theamount, geometry, density, and/or composition of material that mayadsorb or otherwise coat all or part of an electrode or sensor.

As used herein, the term “environmental factors” refers to propertiesand/or factors other than the analyte concentration that affect themeasured electrochemical signal. Examples include, but are not limitedto, electrode area, extent of electrode fouling, dielectric of thesample, temperature, and ionic concentration of the sample.

As used herein, the term “electrolytic contact” refers to having anelectrochemical system comprised of at least one electrode deployed in amanner so as to gather electrochemical information from a sample.Examples include, but are not limited to, an electrode in physicalcontact with a sample; an electrode separated from a sample by amembrane, a film, or other material; and an electrode separated from asample by an aqueous medium. Examples of electrochemical informationinclude Faradaic current, nonfaradaic current, and chemical potential.

As used herein, the term “electrochemical system” refers to a systemcomprised of at least one electrode used to gather electrochemical data.Examples of electrochemical systems include two-electrodeconfigurations; three-electrode configurations; and electrode arrays.

As used herein, the term “electrode set” refers to an electrochemicalsystem comprised of at least one electrode.

As used herein, the term “spectral analysis” refers to a method ofanalyzing the spectral content of a signal or portion of a signal.Examples of methods used for spectral analysis include FT, FFT, DFT,DTFT, and WT.

FIGS. 5-7 show an illustrative embodiment of a method and system fordetermining the signal variation due to environmental factors that alteran electrochemical signal in response to an applied voltage waveform.For example, signal variations caused by environmental factors may bequantified and corrected, if necessary, by altering the apparentmeasured analyte concentration estimate. FIGS. 5 and 6 illustrateembodiments of the method in flow diagram form.

FIG. 7 shows a more detailed example of a system for carrying out themethods of FIGS. 5 and 6, but it should be understood that the methodsof FIGS. 5 and 6 could be implemented by any number of different systemsand apparatus. For example, the system of FIG. 7 could in turn beimplemented as a handheld tester, such as for testing glucoseconcentrations in blood.

FIG. 7 illustrates an exemplary method for identifying and quantifyingthe capacitive properties of the TSI according to an embodiment of thepresent invention. All arrows represent a set of communication channels,unless otherwise labeled, and can include but are not limited to,electrical transmission via physical conductors, wireless transmission,and multiple channels of communication. The following steps outline oneexemplary apparatus and one exemplary process that illustrates theinvention.

1. A set of appropriate transducers 6 is deployed in a manner that isappropriate for detecting ESSs 4 in a sample 2. In this example, thetransducers 6 are electrodes that are placed in electrolytic contact atthe transducer-sample interface 38 with a sample 2 containing multipleESSs 4, labeled as ESS 1, ESS2 and ESS n, where n signifies a numberthat represents an ESS that is unique from the other ESSs in the sample2. Other examples of transducers may include electrodes with membranes,chemically-modified electrodes, or other elements that can be used aselectrochemical transducers.

2. A control signal 34 is applied to transducer 6 from a transducercontrol apparatus 12 which may be processed by an optional filteringprocess 10 such as a circuit or a computation apparatus that executesthe filtering process. The filtering process 10 may be part of thetransducer control apparatus 12. One benefit of a filter would be toremove unwanted noise from the applied signal. In this embodiment, thecontrol signal 34 is a voltage potential waveform that is applied by atransducer control apparatus 12 in the form of a potentiostat circuit. Apotentiostat is a circuit that is commonly used to control and recordelectrochemical data and is explained in “Electrochemistry: Principles,Methods, and Applications”, 1^(st) ed. Oxford University Press, 1993 byC.M.A. Brett and A.M.O. Brett.

3. The time-domain signal 36 (that is, the current signal that isgenerated, as a function of time) from the transducers 6 with thetransducer control apparatus 12 is measured and, if needed, is stored.An optional filtering process 8 may be part of this process, andfurthermore may be part of the transducer control apparatus 12. Thefiltering process may be analogous to figure item 10 and would providethe useful benefit of removing unwanted signal noise.

4. The signal is optionally filtered using a filtering process 14. Oneexample of such a filter includes an anti-aliasing filter used inconjunction with the process of converting analog signals to digitalsignals. Other examples of filters obvious to one skilled in the artinclude high-pass filters, low-pass filters, band-pass filters, andband-stop filters.

5. The signal is converted from analog to digital form to enable theprocessing of the signal by a computing apparatus 18 using an ADC 16.This example illustrates the use of a digital computing apparatus toperform part of the invention method; however, a digital computingapparatus is used as an example and does not limit the invention.Examples of the computing apparatus 18 include analog circuits, digitalcircuits, microprocessors and microcontrollers. Examples of currentlyused microcontrollers include Hitachi H8/3887, Texas Instruments3185265-F, Sierra SC84036CV, Amtel S5640 ASIC, NEC FTA-R2 ACIC, HitachiH8/3847, Panasonic MN101C097KB1, ASIC (built around Intel 8051), etc.

6. The signal is filtered using a filtering process 20. Such a filtermay be used to reshape and/or transform the signal to a more optimalwaveform that is better suited for the other computational processes inthe computing apparatus 18. One example of such a filter may be aband-pass filter that just selects a particular range of frequencies andsuppresses other frequencies from the measured signal. Such a filterwould be useful if the current signal were generated by a nonlinearelectrochemical process, resulting in higher frequency components inaddition to the fundamental frequency that was used as the voltagestimulus.

7. The spectral content of the signal is characterized in teams of boththe magnitude and phase angle of each frequency component of interestusing a spectral analysis process 22; a commonly used process is the FTand includes related processes such as the FFT, DFT, WT, DTFT. One ofordinary skill will recognize the possibility of using other spectralanalysis processes as appropriate for the system under consideration.

8. The signal contribution from ESSs that give rise to capacitiveproperties of the system in the measured signal is determined using acapacitive property quantification process 24. For example, oneembodiment of such a process 24 is:

a. Compute the high frequency signal spectrum and quantify the relevantfeatures of this portion of the spectrum, since the high frequencyportion of the spectrum is expected to contain more information aboutthe capacitive properties of the signal. In one example, the magnitudeand phase angle of the frequency spectrum are used as the features ofthe signal.

b. Compute the values associated with capacitive properties of thesignal; such properties may include but are not limited to theimpedance, the reactance, the resistance, and the capacitance, utilizingany external data source A 26 that may be necessary.

9. Compute other values that may be derived from the above computationsusing a derived quantity computation process that may make reference toan external data source B 30. Data source A 26 and data source B may bethe same data source. They represent means of storing information andcan be different data structures within a single memory unit. Examplesof information that the external data source B 30 may contain includeproperties of the transducer such as the electrode area and frequencyresponse curves for different applications; properties of the samplesuch as the ionic strength, viscosity, density, double-layer capacitancevalues, and dielectric constant; properties of any material in thesample that may cause electrode fouling such as dielectric constants andrelated values; properties such as dielectric constants or thickness orcapacitive properties of any membrane or similar material that may coverthe electrode. Examples of derived quantities include computing theconcentration of the analyte by comparison to calibration data,computing the effective electrode area, computing the extent ofelectrode fouling, and computing the dielectric and permittivityconstants of the background electrolyte by comparison to equations andother data describing the composition of the electrolyte.

10. The derived quantities from the derived quantity computation process28 are used in a correction process 40 that corrects for distortions orvariations the measured signal 36 caused by environmental variations andphysical variations which have been identified and quantified above. Anexample of a correction process is to scale the estimated analyteconcentration that was determined by the derived quantity computationprocess 28 by a value that reflects the change in effective electrodearea or by a value that reflects the extent of electrode fouling, asdetermined by the capacitive property quantification process 24.

11. The output 32 is generated in a usable form. Examples includetransmitting the concentration values of all ESSI in electronic formator displaying the estimated analyte concentration in an LCD display tothe user of the sensor.

FIGS. 5 and 6 refer to the processes that are implemented in the systemof FIG. 7. Referring to FIG. 5, a waveform shape may be selected (step100) and applied to an electrode system to measure samples containingknown concentrations of the analyte of interest. In the first exampleembodiment, the electrode area is varied systematically with noelectrode fouling as different concentrations of analyte are measured(steps 105, 110, 115, 120, 125) to gather calibration data. In thesecond example embodiment, the electrode area is kept constant, but theextent of electrode fouling is varied, as different concentrations ofanalyte are measured (steps 105, 110, 130, 135, 140) to gathercalibration data.

In these example embodiments, the stimulus waveform is selected (step100) so that a signal component that depends on the concentration of thedesired analyte and a signal component that depends on environmentalfactors are measured. In this example, the two environmental factorsthat are illustrated are the effective electrode area and the extent ofelectrode fouling. According to an embodiment, the stimulus waveform ischosen such that the capacitive properties of the electrochemical systemare extractable (step 110) and quantifiable. In an another embodiment,the stimulus waveform is chosen such that the capacitive signalcomponents are much more sensitive to the environmental factors (e.g.electrode area and electrode fouling) and much less sensitive to theanalyte concentration, thereby allowing for monitoring the effects ofelectrode area or electrode fouling that is independent of analyteconcentration. This allows for quantification of just the environmentalvariation without dependence on the analyte concentration.

According to an embodiment that corrects for variations in effectiveelectrode area, calibration data may be gathered by making measurementswith electrodes of different known effective areas with samplescontaining known different analyte concentrations (step 115). Formeasurements made with each electrode area, calibration curves may beconstructed that relate the Faradaic signal component to theconcentration of the analyte in the sample (step 120). Calibrationcurves may also be constructed that relate the capacitive signalcomponent to variations in electrode area when measuring samples withdifferent analyte concentrations (step 120). In the system of FIG. 7,the filter process 20, spectral analysis process 22, and capacitivequantification process 24 can be used to quantify the capacitive signalcomponent.

According to an embodiment, equations may be constructed to correct thecalibration curve that estimates the analyte concentration based on aFaradaic signal component for errors that may arise from variations inthe effective electrode area of the sensor using the capacitivecalibration data that quantifies the effective electrode area (step125).

Once the calibration curves and correction equations have beendetermined, in the system of FIG. 7, this information may be stored indata source A 26 and/or in data source B 30. The correction equationscan be used in the correction process 40 to correct for an erroneousanalyte estimate that has been altered by variations in the effectiveelectrode area when a measurement is made in a sample of unknown analyteconcentration and with an electrode where the effective electrode areais not known.

Referring to FIGS. 6 and 7, transducers 6 (illustrated as electrodes)may be placed into contact with the sample 2 containing unknownconcentration of analyte, indicated by ESS 4. The selected stimuluswaveform (step 105) may be applied to the electrodes by thepotentiostat, indicated as the transducer control apparatus 12. Theapplication of this stimulus waveform is illustrated as signal 34. Theresponse signal 36 may be measured and analyzed by the computingapparatus 18 to quantify the capacitive and Faradaic signal components(step 110). The capacitive signal components, which have just beencomputed by spectral analysis process 22 and capacitive propertyquantification process 24, may be compared to calibration data stored indata source A 26 to determine effective electrode area (step 200). TheFaradaic signal component may then be compared with calibration datafrom data source B 30 to estimate the analyte concentration in thesample (step 225).

This analyte estimate is not yet corrected for errors that may resultfrom variations in effective electrode area. The correction equationsfrom data source B 30 may used with the initial analyte estimates in acorrection process 40 to adjust the estimated analyte concentration toaccount for changes in effective electrode area (step 205). Thecorrected analyte estimate may then be output 32 in a usable form, suchas using an LCD display (step 210).

According to an embodiment that corrects for variations in the extent ofelectrode fouling, calibration data may be gathered by makingmeasurements with electrodes of different known extents of fouling withsamples containing known different analyte concentrations (step 130).For these measurements, calibration curves may be constructed thatrelate the Faradaic signal component to the concentration of the analytein the sample (step 135). Calibration curves may also be constructedthat relate the capacitive signal component to variations in the extentof electrode fouling when measuring samples with different analyteconcentrations (step 135). In the system of FIG. 7, the filter process20, spectral analysis process 22, and capacitive quantification process24 may be used to quantify the capacitive signal component.

According to an embodiment, equations are constructed to correct thecalibration curve that estimates the analyte concentration based on aFaradaic signal component for errors that may arise from variations inthe extent of electrode fouling using the capacitive calibration datathat quantifies the extent of electrode fouling (step 140).

Once the calibration curves and correction equations have beendetermined, in the system of FIG. 7, this information may be stored in,for example, data source A 26 and/or in data source B 30. The correctionequations may be used in the correction process 40, for example, tocorrect for an erroneous analyte estimate, such as one that has beenaltered by variations in the extent of electrode fouling when ameasurement is made in a sample of unknown analyte concentration andwith an electrode where the extent of fouling is unknown.

Referring to FIGS. 6 and 7, then, the electrode system (illustrated astransducers 6) may be placed into contact with the sample 2 containingunknown concentration of analyte (illustrated as ESS 4). The selectedstimulus waveform (step 105) may be applied to the electrodes by thepotentiostat (illustrated as transducer control apparatus 12). Thiswaveform is illustrated as signal 34. The response signal 36 may bemeasured and analyzed by the computing apparatus 18 to quantify thecapacitive and Faradaic signal components (step 110). The capacitivesignal components, which have just been computed by spectral analysisprocess 22 and capacitive property quantification process 24, arecompared to calibration data stored in data source A 26 to determine theextent of electrode fouling (step 215). The Faradaic signal component iscompared with calibration data from data source B 30 to estimate theanalyte concentration in the sample (step 225). This analyte estimate isnot yet corrected for errors that may result from variations in theextent of electrode fouling. The correction equations from data source B30 are used with the initial analyte estimates in a correction process40 that adjusts the estimated analyte concentration to account forchanges in the extent of electrode fouling (step 220). The correctedanalyte estimate is then output 32 in a usable form, for example beingdisplayed to the user in an LCD display (step 210).

In this example, the stimulus waveform is first used to gathercalibration data from samples that contain different concentrations ofanalyte and with different environmental factors to form correctionequations. This same waveform is applied to the sample containingunknown concentrations of the analyte and unknown environmental factors.In this example, ferrocyanide is identified as the desired (or target)analyte and effective electrode area and extent of electrode fouling areidentified as illustrative environmental factors.

The stimulus waveform may be a DC potential with a high frequency smallamplitude AC sine wave superimposed. The phrase “high frequency smallamplitude sine wave,” as used herein, denotes a sinusoidal waveform(typically below 50 mV of peak-to-peak amplitude and typically above 100Hz) that will generate a signal response from the sample that can beapproximated by a linear relationship with the applied potential. Aexemplary waveform format is shown in FIG. 11. A DC potential is appliedto the electrode and an AC sinusoidal voltage 510 is superimposed ontothis DC potential. The amplitude of this AC voltage 510 need not be keptbelow 50 mV and can be any value that gives rise to a usable signal. Thefrequency of the AC potential 510 may be adjusted as is needed to elicitthe capacitive features of the electrochemical system, and the range maybe adjusted as is needed for the system under consideration and does notlimit the scope of the invention in any way. The AC voltage 510 may thenbe stepped through a range of frequencies to probe the spectralcharacteristics of the electrochemical system over a spectral range. Oneof ordinary skill in the art will recognize the possibility of usingother waveforms that can extract capacitive properties of theelectrochemical system including using different frequencies of stimulusand different shapes of waveforms.

The application of the DC and AC potentials may result in the generationof a DC and AC current, where the AC current may be comprised of thesame frequency as the stimulating AC potential. If the electrochemicalsystem is linear, then the resulting AC current will contain only thesame frequency component as the stimulating AC potential. However, ifthe electrochemical system is not completely linear, then there may beother frequency components in the AC current signal.

At the stimulating frequency, the phasor representation of the voltageand current signals can be given by:

{right arrow over (V)}=V _(r) +jV _(i)

{right arrow over (I)}=I _(r) +jI _(i)

where {right arrow over (V)} and {right arrow over (I)} are vectors,called phasors, that represent the magnitude and phase angle informationof the AC voltage and AC current signals, respectively, at a particularfrequency of interest. The phasors represent this information as acomplex number where the subscripts r and i represent the real andimaginary components, respectively. Furthermore, the magnitude and phaseangle of the phasors can be given by:

${\angle \; V} = {\arctan \left( \frac{V_{i}}{V_{r}} \right)}$${\angle \; I} = {\arctan \left( \frac{I_{i}}{I_{r}} \right)}$${V} = \sqrt{\left( V_{r} \right)^{2} + \left( V_{i} \right)^{2}}$${I} = \sqrt{\left( I_{r} \right)^{2} + \left( I_{i} \right)^{2}}$

The understanding with the use of phasors is that the information refersto a particular frequency of interest. Phasor analysis of sinusoidalsignals is a well known method, as explained in B. P. Lathi, “LinearSystems and Signals”, Berkeley-Cambridge Press, Carmichael, Calif. 1992.One example of using AC sine wave signals illustrates the use of probingthe electrochemical system over a range of frequencies. According to anembodiment, an exemplary method of stepping through a range offrequencies may include the following steps:

1. Start the oscillation of the voltage at a particular frequency;

2. Record the resulting current signal when the readings stabilize;

3. Change the oscillation frequency to a new value; and

4. Repeat steps 2-4 as needed to cover the range of interest.

One example of stepping through a range of frequencies includes startingthe oscillation at a particular frequency and then increasing thefrequency logarithmically. However, one of ordinary skill in the artwill recognize the possibility of starting at a higher frequency anddecrementing the frequency through the desired range or the possibilityof stepping through the frequencies in a linear fashion rather than alogarithmic fashion.

The spectral analysis process 22 can compute the necessary phasorinformation for the voltage and current signals according to anembodiment of the present invention. In one example, each frequency ofstimulation is applied to the transducers in steps, so one possiblemethod of spectral analysis is computing the phasor information for eachfrequency of stimulus subsequent to measurement at that frequency.Another example of a possible method is to store all the measured andapplied signal data first and then perform all the computation in onestep at the end of the data acquisition steps. Another example of apossible method is in the case of a linear electrochemical system, allthe frequencies of interest may be superimposed simultaneously as thevoltage stimulus; then the resulting current signal may be expected tocontain responses at all the stimulating frequencies. Since that wouldbe a case for a linear system, then performing a FT analysis on theentire signal at once would reveal the phasor information for eachfrequency of interest simultaneously. One of ordinary skill in the artwill recognize the possibility of executing the spectral analysisprocess 22 in many different embodiments. For example, it may bepossible to perform spectral analysis by measuring the correlationbetween the measured signal and a set of reference sinusoid waves ofdifferent frequencies and different phase shifts.

The phasor information for the current and voltage AC signals may thenbe used by the capacitive property quantification process 24. One methodof quantifying the capacitive properties includes, but is not limitedto, computing the immittance value of the electrochemical system. Theimmittance may be computed in terms of the impedance, given by {rightarrow over (Z)}, or the admittance, given by {right arrow over (Y)}. Inone example, the admittance is calculated as follows:

$\overset{->}{Y} = \frac{\overset{->}{I}}{\overset{->}{V}}$${\overset{->}{Y}} = \frac{\overset{->}{I}}{\overset{->}{V}}$${\angle \; \overset{->}{Y}} = {{\angle \; \overset{->}{I}} - {\angle \; \overset{->}{V}}}$$\overset{->}{Y} = \frac{1}{\overset{->}{Z}}$

where all values are taken to be given at a particular frequency.

The admittance values may be used for the computation of capacitiveproperties. An ideal capacitor as is traditionally considered inelectronic circuit analysis will have the following admittanceproperties:

{right arrow over (Y)}(ω)=jωC

|{right arrow over (Y)}(ω)|=ωC

∠{right arrow over (Y)}(ω)=90°

where C is the capacitance, which describes the capacity of the systemto store charge, j is the imaginary number √{square root over (−1)}, andω is the frequency of the sinusoidal stimulus, given by ω=2πf where f isthe frequency in hertz.

An electrochemical system may also a capacitive component, although theproperties may not follow those of an ideal electronic capacitor. Thiscapacitive property may arise from several considerations including, butnot limited to the following:

1. placing an electrode in a sample that contains charged speciesapproximates some of the electrical properties of an ideal electroniccapacitor;

2. placing an electrode in a sample that contains ESSs which may havedipole moments that approximate some of the electrical properties of anideal electronic capacitor; and

3. varying the electrode potential, or current, over time to approximatesome of the electrical properties of an ideal electronic capacitor byallowing charge to accumulate on the electrode surface and therebycausing the accumulation of the appropriate charges near the electrodesurface in the sample over time.

The origins of the capacitive properties of the electrode-sampleinterface 38 are well understood and are discussed in “Electrochemistry:Principles, Methods, and Applications”, 1^(st) ed. Oxford UniversityPress, 1993 by C.M.A. Brett and A.M.O. Brett. At high frequencymeasurements, the total electrochemical signal may be dominated by thecapacitive components. Therefore, in this example, it is the highfrequency spectrum that is considered for probing the capacitiveproperties of the electrochemical system.

The present invention encompasses several methods for computing thecapacitance of the electrochemical system. One example is to obtain thecurrent signal resulting from a high frequency sinusoidal potentialwaveform. The admittance values revealing the capacitive properties maynot be ideal. Deviations from the ideal capacitor behavior maymaterialize in ways including, but not limited to, the admittance phaseangle not being 90° in the range of frequencies measured. However, theadmittance magnitude spectrum may still be linear when plotted onlog-log axes, as is done in a Bode plot. These are examples of how thecapacitive properties of an electrochemical system may be manifested ina real system and as such are intended to be examples for illustrativepurposes and do not limit the scope of the invention.

In analyzing the capacitive properties of an electrochemical system, thedeviations from ideal capacitance may need to be considered. One exampleof how the variations may be addressed is to consider the component ofthe admittance that is at 90° for each frequency of interest. FIG. 12illustrates this concept. At a particular frequency, the vectorrepresenting the admittance 50 is not the ideal capacitor value of 90°.However, the real component of the vector 54 and the imaginary component52 can be used to deconstruct the total admittance vector 50 into twovectors. Therefore, by considering the value of the imaginary component52 alone, the capacitive component of the total admittance may beselected. This allows for the extraction of just the current signalcomponent that is 90° out of phase with the voltage signal, which can bea measure of the capacitive nature of the electrochemical system. Inthis way, non-ideal characteristics of the CDAS, which may causedeviations from the ideal 90° phase angle, can be minimized in the finalanalysis.

Another example of analyzing nonideal capacitive properties of anelectrochemical system is to consider the magnitude spectrum. In thisexample, the magnitude spectrum in the frequency range that is dominatedby capacitive signals is taken to be linear in a log-log Bode plot. Assuch, the linear nature of the magnitude plot may evince the dominanceof capacitive components in the electrochemical system overnon-capacitive components. In some applications, the slope of themagnitude spectrum may correlate to different properties of the TSI andcan be used to characterize the system.

Some exemplary factors that may affect the capacitive properties of theelectrochemical system include:

1. effective electrode area

2. components that comprise the sample including but not limited toionic makeup of sample, non-ionic makeup of the sample, presence ofvarious ESSs.

3. viscosity of the sample

4. density of the sample

5. extent electrode fouling

6. membranes which may cover the electrode

7. the applied DC voltage

8. the applied AC voltage

9. mass transport in the sample including, convection, diffusion ofsample components, migration of sample components, flow rate of thesample

10. temperature

11. reactions which may occur at the electrode

The measure of the capacitance of the electrochemical system may be usedto probe characteristics of the electrochemical system. One example ofhow this may be embodied is by considering one equation that definescapacitance for a parallel plate capacitor:

$C = \frac{A\; ɛ}{d}$

where C is the magnitude of the capacitance, A is the area of theelectrode, s is the permittivity (and reflects the dielectric propertiesof the system), and d is the distance between the plates of a parallelplate capacitor. In this example electrochemical system, one plate ofthe capacitor may be considered to be the electrode surface and theother plate may be considered to be the plane in the sample thatcontains the layer of spatially distributed charges. This is awell-known description of the TSI, commonly referred to as the“double-layer” and is discussed in “Electrochemistry: Principles,Methods, and Applications”, 1^(st) ed. Oxford University Press, 1993 byC.M.A. Brett and A.M.O. Brett. One of ordinary skill in the art willrecognize the possibility of having other equations relating thecapacitance to the physical properties of the electrochemical setup. Forexample, a cylindrical capacitor equation may be more appropriate for awire electrode. Such relationships that are necessary and appropriatefor the system under consideration may be supplied by the data source A26. Assuming the above equation to describe the capacitance of theelectrochemical system under consideration in this example, it ispossible to equate the admittance with the capacitance as follows:

${{\overset{->}{Y}(\omega)}} = {{\omega \; C} = \frac{\omega \; A\; ɛ}{d}}$

Thus, if the magnitude of the admittance is known at a given frequency,then there remain three unknowns, namely A, ε, and d. Utilizing anexternal data source A 26 which may contain the values of two of theseunknowns, then the third may be computed by the above equation by thecapacitive property quantification process 24. As a further example, thevalues of the parameters describing the capacitance need not be knownexplicitly. Instead, they may be known in aggregate and the change incapacitance due to one of these parameters may also be used as a measureof quantifying capacitive properties in process 24. The benefit of thisanalysis is that often several of these parameters may be known, but onemay change without knowledge. This characteristic of the capacitance maybe exploited to correct for variations in the TSI by a correctionprocess 40.

These procedures that measure the capacitive properties of anelectrochemical system may be useful due to the fact that the inherentnature of the measurements lends itself to monitoring primarily physicaland material properties of the environments in which the electrochemicalsystem operates. They help establish an overall metric forcharacterizing the physical and environmental effects of theelectrochemical system and form the basis for developing correctionmechanism 40 that can account for such sources of error and can beextended for more detailed measurements of various purposes, such as:

1. diagnosing the state and condition of an electrode or transducer,including determining effective electrode area

2. determining various characteristics of the electrode foulingscenario, including, but not limited to, the thickness of the foulinglayer, the rate of fouling material buildup, and electrical propertiesof the fouling material.

In practice, a stimulus waveform can be selected through a combinationof experimental trials and theoretical consideration of the processesthat are involved in the detection process. The selection of thewaveform is done in order to achieve certain unique signalcharacteristics generated by a particular analyte and the environmentalfactors. The DC component of the measured signal may be comprised mostlyof Faradaic signal components, which are affected by the analyteconcentration and environmental factors. But, the AC component of themeasured signal may be comprised mostly of capacitive signal components,which are less likely to be affected by the analyte but are responsiveto the environmental factors. Thus, the AC component may be used toindependently gain information about the environmental factors withoutbeing influenced by the analyte concentration.

Factors to keep in mind when choosing a waveform include but are notlimited to: the use of more positive potentials of the working electrodewith respect to the reference electrode will generally increase the rateof oxidation; similarly, use of more negative potentials of the workingelectrode with respect to the reference electrode will generallyincrease the rate of reduction; and when the rate of kinetics is muchfaster than the rate of transport of the analyte (such as by diffusion),further increasing the rate of kinetics by increasing the potential inthe appropriate direction (positive for oxidations or negative forreductions) may not significantly increase the Faradaic current flow;higher frequency AC sine waves may be sensitive to non-Faradaiccapacitive properties than lower frequency AC sine waves.

After selecting the waveform, data may be gathered from samplescontaining different concentrations of the target and with differentenvironmental factors (steps 115 and 130). For example, indistinguishing and determining the influence of effective electrode areaand analyte concentration, one could make five repeated measurementsusing the selected waveform for each of the following concentrations offerrocyanide: 0 mM, 1 mM, 2 mM, 3 mM, 5 mM, 10 mM, 15 mM, 20 mM usingelectrodes of each of the following effective areas: 0.1 mm², 0.2 mm²,0.3 mm², 0.5 mm², 0.7 mm², 10 mm². In another example, in distinguishingand determining the influence of the extent of electrode fouling andanalyte concentration, one could make five repeated measurements usingthe selected waveform for each of the following concentrations offerrocyanide: 0 mM, 1 mM, 2 mM, 3 mM, 5 mM, 10 mM, 15 mM, 20 mM usingelectrodes which have been coated with fouling material of each of thefollowing thicknesses: 10 μm, 20 μm, 30 μm, 50 μm, 70 μm, 100 μm, 150μm, 200 μm, 300 μm, 500 μm. Examples of materials that could be used toemulate different types of fouling include polymers such as celluloseacetate, and polytyramine, or proteins such as bovine serum albumin.

EXAMPLE 1

An example using the method of FIGS. 5 and 6 and system as carried outby, for example, a system of FIG. 7, is now described in terms ofanalyzing the concentration of a sample containing the analyteferrocyanide and variable effective electrode area. The Faradaicreaction that is detected by a DC potential is given by:

FERROCYANIDE→FERRICYANIDE+e−

which is an oxidation reaction. The electrochemical cell may be aconventional 3-electrode set up with a palladium working electrode,platinum counter electrode, and a Ag/AgCl reference electrode. Theworking electrode may be held at a DC potential of −400 mV with respectto the reference electrode. FIG. 2 shows the DC current from twosamples, one containing 10 mM FERRO and the other containing 20 mMFERRO, for measurements made with different effective electrode areas.

FIG. 2 shows the data points 450 that were measured by applying a DCpotential of −400 mV to a sample containing 20 mM ferrocyanide.Measurements 450 were made with electrodes of different effective areas,and the data is plotted in FIG. 2. The X-axis shows the effectiveelectrode area of the electrode that was used to make the measurementsand the Y-axis shows the value of the DC current that was measured.Using the same electrodes, measurements were then performed in samplescontaining 10 mM ferrocyanide and are shown as data points 455. Thisfigure illustrates the problem of measuring amperometric signals using aDC potential. The measured signal is affected by both the analyteconcentration and the effective electrode area. One equation that may beused to describe this relationship is:

I=αA_(e)[FERRO]

where α is a proportionality constant, A_(e) is the effective electrodearea, and [FERRO] is the concentration of ferrocyanide in the sample.One of ordinary skill in the art would recognize the possibility ofother relationships that may exist, and these relationships could bedetermined by a combination of theoretical and experimentalinvestigation. FIG. 10 illustrates this relationship for two values ofA_(e). Data points 500 are the DC current measurements made with anelectrode of A₃=0.8925 mm². The equation of the calibration curve forthis A_(e) is:

I=109.21 [FERRO]

Data points 505 are the DC current measurements made with an electrodeof A_(e)=1.575 mm². The equation of the calibration curve for this A_(e)is:

I=171.13 [FERRO]

Thus, if measurements are made with an electrode under the assumptionthat A_(e)=1.575 mm², the ferrocyanide concentration would be estimatedwith the equation:

[FERRO]=1/171.13

where I is the measured DC current in nA and [FERRO] is the estimatedferrocyanide concentration in mM.

However, if the effective electrode area were unknowingly not equal to1.575 mm², then the calculated ferrocyanide estimate could be incorrect.For example, if A_(e) was actually 0.8925 mm², then a sample containing20 mM ferrocyanide would yield a measured current signal of 2188 nA, assown in FIG. 10 by data points 500. Examples of how such a change inA_(e) might occur include errors in manufacturing or partial contact ofthe sample with the electrode. Using the assumption that A_(e) is 1.575mm², the estimated ferrocyanide concentration would be calculated by thecalibration equation as:

[FERRO]=2188/171.13=12.3 mM

This illustrates the type of error in estimating analyte concentrationthat may occur if the effective electrode area were to become alteredunknowingly. However, being able to obtain a measure of the effectiveelectrode area would allow for correcting the analyte estimate for suchchanges in the measurement system.

To probe the effective electrode area, in this example a 1000 Hz sinewave of 40 mV peak to peak amplitude was superimposed onto the DC biaspotential of −400 mV (step 100), as shown in curve 510 of FIG. 11. Thiswaveform was then applied to the electrode system (step 105). TheFourier Transform of the resulting current signal was taken to selectthe 1000 Hz AC sinusoidal component (step 110), since the capacitiveproperties of the system are expected to be reflected in high frequencycomponents of the signal. In this example, since the amplitude of the ACsine wave potential is kept constant at 40 mV peak to peak, it issufficient to just use the AC current values in the calculation ofcapacitive properties instead of computing the admittance values, as isdefined by the mathematical relationship between AC admittance, ACcurrent, and AC potential discussed above.

FIG. 13 shows capacitive signal data represented by the imaginarycomponent of the 1000 Hz AC current signal gathered with electrodes ofdifferent effective areas in a sample of 10 mM ferrocyanide (black datapoints 515) and a sample of 20 mM ferrocyanide (white data points 520).It is clear from this data that there is a linear relationship betweenthe capacitive signal component and the effective electrode area andthat furthermore, the capacitive signal data is not significantlyinfluenced by the concentration of ferrocyanide in the sample.

An equation that relates the imaginary AC current to the effectiveelectrode area (step 120) that is independent of analyte concentrationis:

I _(i,AC)=(818.26)(A _(e,actual))−14.33

where I_(i,AC) is the imaginary component of the AC current at 1000 Hz,A_(e,actual) is the actual effective electrode area.

One equation that may be used to describe the measured Faradaic DCelectrode current (I_(F)) to be used in constructing calibration curvesfor estimating ferrocyanide concentration in a sample is:

$I_{F} = {{\alpha \; {{A_{e,{expected}}\lbrack{FERRO}\rbrack}\lbrack{FERRO}\rbrack}} = {\left( \frac{1}{\alpha \; A_{e,{expected}}} \right)I_{F}}}$

where A_(e,expected) is the value of the effective electrode area thatthe electrode is expected to have. This is because when calibrationcurves were constructed by using an electrode system (step 120) based onFaradaic signal data to relate measured Faradaic signal to ferrocyanideconcentration, an electrode of effective area A_(e,expected) was used.If an unknown sample is measured with an electrode of A_(e,expected),and these calibration curves are used to estimate the ferrocyanideconcentration in the sample (step 225), then one may expect that theestimated ferrocyanide concentration is representative of the actualconcentration in the sample. However, if the unknown sample is measuredwith an electrode of effective area that is not equal to A_(e,expected),then an erroneous estimate of ferrocyanide may likely result.

Thus, one correction equation (step 125) that may be used to adjust theestimated ferrocyanide concentration (step 205) for variations in theeffective electrode area is:

$\lbrack{FERRO}\rbrack_{c} = {{\left( \frac{1}{\alpha \; A_{e,{expected}}} \right)\left( \frac{A_{e,{expected}}}{A_{e,{actual}}} \right){I_{F}\lbrack{FERRO}\rbrack}_{c}} = {\left( \frac{A_{e,{expected}}}{A_{e,{actual}}} \right)\lbrack{FERRO}\rbrack}_{u}}$$A_{e,{actual}} = \frac{I_{i,{AC}} + 14.33}{818.26}$

where A_(e,actual) is computed as described above. [FERRO]_(c) is theferrocyanide concentration corrected for variation in the effectiveelectrode area and [FERRO]_(u) is the uncorrected ferrocyanideconcentration.

Continuing with the illustrative example, if calibration curves forestimating ferrocyanide concentration were constructed with an expectedelectrode area of that A_(e,expected)=1.575 mm², and measurements weremade in a sample containing 20 mM ferrocyanide using an electrode withA_(e,actual)=0.8925 mm², an erroneous estimate of ferrocyanideconcentration would result, as discussed above, giving[FERRO]=2188/171.13=12.3 mM. However, using the capacitive signal data,represented by the imaginary component of the 1000 Hz AC sinusoidalcurrent, the estimated ferrocyanide concentration may be corrected forthe variation in effective electrode area. As shown in FIG. 13 by datapoint 515, a sample containing 20 mM ferrocyanide measured by anelectrode with A_(e,actual)=0.8925 mm² yields I_(a,AC)=680 nA. Thus,

$A_{e,{actual}} = {\frac{I_{i,{AC}} + 14.33}{818.26} = {\frac{680 + 14.33}{818.26} = {{0.850\mspace{14mu} {{mm}^{2}\lbrack{FERRO}\rbrack}_{c}} = {{\left( \frac{A_{e,{expected}}}{A_{e,{actual}}} \right)\lbrack{FERRO}\rbrack}_{u} = {{\left( \frac{1.575}{0.850} \right)12.3} = {22.8\mspace{14mu} {mM}}}}}}}$

thereby yielding a corrected estimate of 22.8 mM ferrocyanide ascompared to an uncorrected estimate of 12.3 mM ferrocyanide,representing nearly a three-fold reduction of error.

This illustrates one exemplary embodiment that uses capacitive signalinformation to correct for measurement errors arising from variations ineffective electrode area. Although this example was illustrated with onefrequency of sine wave, improvements to this method may be realised byusing information from multiple frequencies of sinusoidal stimuli,covering a range of frequencies to construct a set of correctionequations to be used. Another example of an improvement is to constructcalibration curves with a larger matrix of data. FIGS. 10 and 13illustrated calibration data from samples that contained two differentconcentrations of ferrocyanide; however, calibration data may beacquired from samples comprised of a larger selection of differentconcentrations of ferrocyanide to create a more refined set ofcalibration curves. Similarly, data may be acquired from electrodes withmany more different effective areas to create a more refined set ofcalibration curves.

EXAMPLE 2

An example using the method of FIGS. 5 and 6 and system as carried outby, for example, a system of FIG. 7, is now described in terms ofanalyzing the concentration of a sample containing the analyteferrocyanide and variable extent of electrode fouling. As in Example 1,the Faradaic reaction that is detected is the oxidation of ferrocyanideto ferricyanide, and an equivalent 3-electrode electrochemical system isused where the working electrode is a platinum electrode of 3.14 mm². Inthis example, the effective electrode area may be kept constant and theextent of electrode fouling is varied to illustrate the effect offouling on the measured signal and the estimated ferrocyanideconcentration. A method is described to use capacitive signalinformation to correct for errors in ferrocyanide estimation that mayarise due to electrode fouling.

The working electrode was fouled by coating the whole electrode areawith a cellulose acetate (“CA”) membrane. The extent of electrodefouling was varied for two cases. In one case, CA was dissolved inacetone in the proportion of 10 mg cellulose acetate per 1 mL acetone.One μL of this solution was drop-coated onto the working electrode so asto cover the entire platinum surface. The solution was allowed to dry,forming a coating of cellulose acetate, giving a total of approximately10 μg of CA. In a second case, CA was dissolved in acetone in theproportion of 3.33 mg CA per 1 mL acetone. One μL of this solution wasdrop-coated onto the working electrode so as to cover the entireplatinum surface. The solution was allowed to dry, forming a coating ofCA that contained approximately ⅓ the amount of cellulose acetate,approximately 3.33 μg CA. Thus, in this example, the amount of CA wasvaried to emulate different extents of electrode fouling; theexpectation being that a greater extent of electrode fouling may beemulated by coating the electrode with a greater amount of celluloseacetate.

FIG. 3 shows calibration curves that were constructed by applying a DCpotential of −400 mV to a sample containing different concentrationsferrocyanide using an electrode with no fouling (data points 470), 3.33μg CA of fouling (data points 480), and 10 μg CA of fouling (data points490). It can be seen that the measured DC current signal, which isdominated by the Faradaic current component from the oxidation offerrocyanide, depends on both the concentration of ferrocyanide and theextent of electrode fouling. One equation of the calibration curve thatmay be used to describe this relationship is:

I _(DC) =αE _(f1) A _(e)[FERRO]+βE _(f2)

where α and β are constants, A_(e) is the effective electrode area,E_(f1) is a measure of how the extent of electrode fouling affects theslope of the calibration curve, E_(f2) is a measure of how the extent ofelectrode fouling affects the intercept of the calibration curve, I_(DC)is the measured DC current, and [FERRO] is the concentration offerrocyanide in the sample. One of ordinary skill in the art wouldrecognize the possibility of other relationships that may exist, andthese relationships could be determined by a combination of theoreticaland experimental investigation.

In the example of no fouling (data points 470), one equation thatdescribes the calibration curve may be given as:

I _(DC)=0.8757[FERRO]+1.6

A_(e)=3.14 mm²

αE _(f)=0.279 μAmm⁻² mM

In the example of 3.33 μg CA of fouling (data points 480), one equationthat describes the calibration curve may be given as:

I _(DC)=0.664[FERRO]+0.1717

A_(e)=3.14 mm²

αE _(f)=0.211 μAmm⁻² mM

In the example of 10 μg CA of fouling (data points 490), one equationthat describes the calibration curve may be given as:

I _(DC)=0.1729[FERRO]+0.2703

A_(e)=3.14 mm²

αE _(f)=0.055 μAmm⁻² mM

It can be seen that the extent of electrode fouling affects both theslope and the intercept of the calibration curves. FIG. 15 is an exampleof how the relationship between the extent of electrode fouling and theparameters of the linear calibration curve, which in this example arethe slope and intercept, can be expressed. Data points 540 represent thevalue of the slope of the calibration curve that relates [FERRO] toI_(DC) for different extents of electrode fouling, given by the quantityαE_(f1)A_(e); data points 545 represent the value of the intercept ofthe calibration curve that relates [FERRO] to I_(DC) for differentextents of electrode fouling, given by the quantity βE_(f2). One exampleset of equations to describe these relationships is:

I _(DC) =αE _(f1) A _(e)[FERRO]+βE _(f2)

αE _(f1) A _(e)=−0.0708(M _(CA))+0.8853

βE _(f2)=0.0444(M _(CA))²−0.5767(M _(CA))+1.6

where M_(CA) is the mass of CA used to foul the electrode in micrograms.One of ordinary skill will recognize that other equations andrelationships may be used, depending on the nature of the data.

FIG. 14 further illustrates the relationship between the measuredcurrent, ferrocyanide concentration, and the extent of electrode foulingfor three concentrations of ferrocyanide using electrodes with threedifferent extents of fouling. Data points 525 are from samplescontaining 5 mM ferrocyanide, data points 530 are from samplescontaining 3 mM ferrocyanide, and data points 535 are from samplescontaining 2 mM ferrocyanide. The data are plotted in FIG. 14 with theY-axis representing the reciprocal of the measured DC current. In thisexample, such a representation allows for an approximately linearrelationship to be observed between the amount of CA used to foul theelectrode and the measured DC current. One of ordinary skill willrecognize that other relationships may exist, depending on the nature ofthe electrochemical system and the nature of the fouling. In the exampledata illustrated in FIG. 14, the relationship between the DC current andthe extent of fouling may be given as:

${\begin{matrix}{\frac{1}{I_{DC}} = {{0.1317M_{CA}} + 0.275}} \\{I_{DC} = \frac{1}{{0.1317M_{CA}} + 0.275}}\end{matrix}\mspace{14mu} {for}\mspace{14mu} {samples}\mspace{14mu} {with}\mspace{14mu} 2\mspace{14mu} {mM}\mspace{14mu} {ferrocyanide}};$${\begin{matrix}{\frac{1}{I_{DC}} = {{0.1033M_{CA}} + 0.1871}} \\{I_{DC} = \frac{1}{{0.1033M_{CA}} + 0.1871}}\end{matrix}\mspace{14mu} {for}\mspace{14mu} {samples}\mspace{14mu} {with}\mspace{14mu} 3\mspace{14mu} {mM}\mspace{14mu} {ferrocyanide}};$${\begin{matrix}{\frac{1}{I_{DC}} = {{0.067M_{CA}} + 0.1279}} \\{I_{DC} = \frac{1}{{0.067M_{CA}} + 0.1279}}\end{matrix}\mspace{14mu} {for}\mspace{14mu} {samples}\mspace{14mu} {with}\mspace{14mu} 5\mspace{14mu} {mM}\mspace{14mu} {ferrocyanide}};$

where I_(DC) is the DC current in microamps and M_(CA) is the mass of CAused to foul the electrode in micrograms.

Thus, if measurements are made with the assumption that there is noelectrode fouling, then the calibration curve representing this casecould be used. However, if the electrode is fouled to an unknown extent,then an incorrect ferrocyanide estimate may be computed. For example, ifthe electrode were fouled by 3.33 μg of CA and measurements were made ina sample containing 5 mM ferrocyanide, then according to FIG. 14,I_(DC)=3.4 μA. Since, in this example, the extent of electrode foulingis not known or quantified, the calibration curve that is used toestimate ferrocyanide concentration is the one constructed with datafrom an unfouled electrode, as described above. Using this calibrationcurve, the following inaccurate estimate of ferrocyanide concentrationis obtained:

$I_{DC} = {{{0.8757\lbrack{FERRO}\rbrack} + {1.6\lbrack{FERRO}\rbrack}} = {\frac{I_{DC} - 1.6}{0.8757} = {\frac{3.4 - 1.6}{0.8757} = {2.1\mspace{14mu} {mM}}}}}$

Thus, a method is needed to quantify the extent of electrode fouling sothat the calibration curve parameters of slope and intercept may bealtered to more accurately estimate the ferrocyanide concentration inthe sample. To probe the extent of electrode fouling, a 1000 Hz sinewave of 40 mV peak to peak amplitude was superimposed onto the DC biaspotential of −400 mV (step 100), as shown in curve 510 of FIG. 11. Thiswaveform was then applied to the electrode system (step 105). In thisexample, since the capacitive properties of the system are expected tobe the dominant component in the high frequency part of the signal, thepeak to peak amplitude of the AC current signal was computed (step 110)by taking the difference between the peak of the sine wave current andthe valley of the sine wave current for the last full measured cycle.

FIG. 16 shows capacitive signal data represented by the peak to peakamplitude of the 1000 Hz AC current signal gathered from samples withdifferent concentrations of ferrocyanide using electrodes with nofouling (data points 550), 3.33 μg of CA used to foul the electrode(data points 555), and 10 μg of CA used to foul the electrode (datapoints 560). It is clear from this data that the AC current amplitude ismostly affected by the extent of fouling and minimally affected byferrocyanide concentration. Thus, the average value of the AC currentwas calculated for each set of measurements made with a fixed extent ofelectrode fouling. FIG. 17 shows that in this example, there is a linearrelationship between this average AC current amplitude (data points 565)and the extent of electrode fouling. One calibration equation todescribe the relationship between the extent of electrode fouling andthe AC current is given by:

I _(AC)=(−8.0598)(M _(CA))+119.05

where I_(AC) is the peak to peak amplitude of the 1000 Hz sinusoidalcurrent component and M_(CA) is the mass of CA used to foul theelectrode.

The AC measurements may be insensitive to and independent of analyteconcentration in this example. So, the AC current value may be used toestimate the extent of electrode fouling. Once the extent of electrodefouling has been estimated, a correction to the concentrationcalibration curve may be made to result in a more accurate estimate offerrocyanide concentration.

Continuing with the example of measuring a sample containing 5 mMferrocyanide with an electrode that has been fouled by 3.33 μg of CA,according to FIG. 16, an AC current of 96.8 μA would be recorded. Usingthe calibration curve that relates AC current to mass of CA, thefollowing estimate of mass of CA is obtained:

I_(AC) = (−8.0598)(M_(CA)) + 119.05$M_{CA} = {\frac{I_{AC} - 119.05}{- 8.0598} = {\frac{96.8 - 119.05}{- 8.0598} = {2.76\mspace{14mu} {µg}}}}$

Using this estimated mass of CA as a measure of electrode fouling, thecorrection factors to the calibration curve slope and intercept may bedetermined using the equations described above:

α E_(f 1)A_(e) = −0.0708(M_(CA)) + 0.8853 = −0.0708(2.76) + 0.8853 = 0.690β E_(f 2) = 0.0444(M_(CA))² − 0.5767(M_(CA)) + 1.6 = 0.0444(2.76)² − 0.5767(2.76) + 1.6 = 0.346$\mspace{20mu} {I_{DC} = {{{\alpha \; E_{f\; 1}{A_{e}\lbrack{FERRO}\rbrack}} + {\beta \; {E_{f\; 2}\mspace{20mu}\lbrack{FERRO}\rbrack}c}} = {\frac{I_{DC} - {\beta \; E_{f\; 2}}}{\alpha \; E_{f\; 1}A_{e}} = {\frac{3.4 - 0.346}{0.690} = {4.4\mspace{14mu} {mM}}}}}}$

where [FERRO]c is the estimate of ferrocyanide in the sample that hasbeen corrected for the extent of electrode fouling. The correctedestimate of ferrocyanide is thus 4.4 mM; when compared to theuncorrected estimate of 2.1 mM, the correction method represents nearlya 5-fold reduction of error.

This illustrates one example embodiment that uses capacitive signalinformation to correct for measurement errors arising from variations inthe extent of electrode fouling. Although this example was illustratedwith one frequency of sine wave, improvements to this method may berealized by using information from multiple frequencies of sinusoidalstimuli, covering a range of frequencies to construct a set ofcorrection equations to be used. Another example of an improvement is toconstruct calibration curves with a larger matrix of data. FIGS. 14, 15,16, and 17 illustrate calibration data from electrodes with threeextents of fouling; however, calibration data may be acquired fromelectrodes with a greater selection of different extents of fouling tocreate a more refined set of calibration curves. Similarly, data may beacquired from samples containing many more different concentrations offerrocyanide to create a more refined set of calibration curves. Anotherexample of an improvement is to use the imaginary part of the AC currentsignal, since the imaginary part of the AC signal is expected to reflectthe capacitive properties of the electrochemical system.

EXAMPLE 3

Another example of a useful benefit of capacitance measurements isdetecting when the sample changes. There may be situations in fuel tankstorage where foreign material leaks into these tanks, as sown in FIG.19. For example, it is not uncommon for water to seep into a fuel tankthat contains petrol products. In some situations, the water and petrolare immiscible and each liquid separates into layers within the tank.This is shown in the figure by a layer of petrol 56 with a layer ofwater 58 on top. There may be a layer of air space 60 above that aswell. If an array of electrodes 62, 64, 66, 68, 70, 72, 74 were linedalong the side of the tank, then it may be possible to spatially resolvethe distribution of the water layers within the petrol layers. One wayin which this may be embodied is that by measuring the capacitance ofeach electrode system 62, 64, 66, 68, 70, 72, 74 by measuring the CDAS.In one example, this can be achieved by applying small amplitude highfrequency sine waves to the electrode system and measuring the resultingcurrent. The AC current component will contain capacitive informationabout the electrochemical system. By referencing external data 30 whichcontains the CDAS profiles for a petrol sample and a water sample, thenthe derived quantity computation process 28 can determine which set ofelectrodes were in contact with water samples 72 and 70 and whichelectrodes were in contact with the petrol samples 62, 64, 66, 68, andwhich electrodes were not in contact with either 74. This can then allowfor spatially resolving the amount of water seepage into a petrolstorage tank. In this example, it may be estimated that approximatelyone part of water for two parts of petrol by volume are in the tanksince two sensors 72 and 70 are in contact with water 58 and foursensors 62, 64, 66, 68 are in contact with petrol 56.

One of ordinary skill in the art will also recognize the possibility ofusing other sources of data in computing the values ofcapacitance-related properties of an electrochemical system. One exampleincludes generating a database of capacitance values for differentelectrode configurations and sample configurations. For example, it maybe possible to develop a set of admittance spectra for:

1. different ionic strengths of background electrolyte in a givensample;

2. different thicknesses of a particular membrane or part of a membranethat covers an electrode;

3. different thicknesses of material that may foul an electrode;

4. different samples;

5. different electrode geometry.

One of ordinary skill in the art will also recognize the possibility ofusing other signal parameters to obtain capacitive information about theelectrochemical system. One example includes the initial rate of decayof a measured signal in response to a step potential. Another example isthe amount of hysterisis that is observed when the electrochemicaltechnique of cyclic voltammetry is used.

FIG. 18 shows an illustrative embodiment of a glucose meter that can beused to implement the various methods described above. The meterincludes a test strip connector 600 to connect the test-strip to themeter. The test strip can include, for example, three electrodes(working, reference, and counter).

Signal conditioning circuitry 602 is coupled to the test strip connector600, and performs filtering of the waveform applied to the electrodes inthe test strip. Signal conditioning circuitry 604 performs filtering ofthe resultant current signal from the test strip, and records thecurrent signal. Circuitry 602 and 604 together comprise what is known asa potentiostat circuit. DAC 606 converts digital signals from controller610 to analog signals. ADC 608 converts analog signals into digitalformat for use by controller 610. Controller 610 processes signals inthe meter, for example, by processing current signals sensed by teststrip connector in the manner taught in the foregoing illustrativeembodiments of FIGS. 5 and 6.

Buttons 612 provide a user interface for the user to operate the meter.Power circuit 614 provides power to the meter, usually in the form ofbatteries, and LCD 616 displays the glucose concentration to the user.

It should be noted that the format of the FIG. 18 meter, and the signalprocessing systems and methods taught herein in FIGS. 5-7, can be usedto sense analytes other than glucose. Such applications include:electrochemical immunoassay sensing, industrial gas sensing, waterquality monitoring (biological or toxic metals), sensing of chemical andbiological warfare agents.

The signal processing techniques taught herein can also be applied toexisting sensing devices, such as a existing glucose testers. Thismodification can be in the form of a firmware upgrade to existingcontrollers.

The function of the firmware upgrade is to implement the followingsignal processing techniques taught herein:

1) Applying a customized waveform to the sample. The data that encodesthe shape of the waveform may reside in memory, will be read by themicroprocessor, and the desired waveform may be generated and applied toa digital to analog converter, e.g., DAC 606 of FIG. 18.

2) Read in the resulting current signal. The firmware may instruct themicroprocessor to read in the digitized data from the analog to digitalconverter (sensed from the test strip electrodes), e.g., ADC 608 of FIG.18, and store the digitized data in memory. The firmware may perform thememory management that is needed to read in the desired data.

3) Perform the mathematical operations to implement the signalprocessing. This includes calculating the parameters according to thefirmware's instructions (e.g., compute the Fourier Transform of thesignals), and using these parameter values in the estimation equation(e.g., generated by the methods of FIG. 5 or FIG. 6) to determine theglucose concentration.

Other processes performed by the firmware may be left to the existingfirmware and do not need to be part of the upgrade. For example, thefirmware may also control the display of a result to the user (via theLCD 616 display, for example), and other “behind the scenes” operationsof the meter, e.g., power management, respond to user requests such asscrolling of data, averaging of data, transferring data to a PC, etc.

It will be apparent to those skilled in the art that additional variousmodifications and variations can be made in the present inventionwithout departing from the scope or spirit of the invention.

Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope of theinvention being indicated by the following claims.

1. A method for determining the extent of electrode fouling in animplantable electrochemical sensor comprising at least two electrodes,the extent of electrode fouling being determined from effectiveelectrode area, said method comprising: applying a potential stimulus tothe electrodes to generate a current signal, the potential stimuluscomprising a time-varying potential component superimposed on a constantpotential component; isolating a time-varying current component from thecurrent signal; determining an imaginary part of the time-varyingcurrent component, the magnitude of the imaginary part of thetime-varying current component being linearly related to the effectiveelectrode area; and determining the extent of electrode fouling from thedetermined magnitude of the imaginary part of the time-varying currentcomponent.
 2. The method of claim 1, wherein the effective electrodearea changes as a result of electrode fouling.
 3. The method of claim 1,wherein the measured effective electrode area is used to adjust thecomputation of concentration of an analyte and correct for signaldistortion caused by changes in effective electrode area.
 4. The methodof claim 2, wherein the measured extent of electrode fouling is used toadjust the measured current signal and correct for signal distortioncaused by electrode fouling.
 5. The method of claim 4, wherein theadjustment corrects for a decrease in signal intensity due to fouling.6. The method of claim 3, wherein the adjustment is based on relativechanges from initial analyte estimates.
 7. The method of claim 3,wherein the adjustment is based on reference to an external data source.8. The method of claim 7, wherein the external data source comprisescalibration curves from calibration data gathered from electrodes havingdifferent electrode areas.